Weak axioms of determinacy and subsystems of analysis II

Annals of Pure and Applied Logic 52 (1-2):181-193 (1991)
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Abstract

In [10], we have shown that the statement that all ∑ 1 1 partitions are Ramsey is deducible over ATR 0 from the axiom of ∑ 1 1 monotone inductive definition,but the reversal needs П 1 1 - CA 0 rather than ATR 0 . By contrast, we show in this paper that the statement that all ∑ 0 2 games are determinate is also deducible over ATR 0 from the axiom of ∑ 1 1 monotone inductive definition, but the reversal is provable even in ACA 0 . These results illuminate the substantial differences among lightface theorems which can not be observed in boldface

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Citations of this work

Reverse mathematics: the playground of logic.Richard A. Shore - 2010 - Bulletin of Symbolic Logic 16 (3):378-402.
Determinacy in third order arithmetic.Sherwood Hachtman - 2017 - Annals of Pure and Applied Logic 168 (11):2008-2021.

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References found in this work

Fixed point theory in weak second-order arithmetic.Naoki Shioji & Kazuyuki Tanaka - 1990 - Annals of Pure and Applied Logic 47 (2):167-188.
The Galvin-Prikry theorem and set existen axioms.Kazuyuki Tanaka - 1989 - Annals of Pure and Applied Logic 42 (1):81-104.

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